The former Crystal Palace starlet is now regarded among the most exciting attacking players in Europe.
And Kompany said of Olise on Friday: "What sets him apart is his mentality.
"He's a perfectionist, an extremely fussy guy who gets irritated if every detail isn't perfect. For a coach who strives for excellence, having a player who demands so much of himself makes the job much easier."
Kompany then paid Olise a special compliment, likening him to his former Manchester City teammate Kevin de Bruyne, now with Napoli.
He added: "I often see him in Kevin. His precision in his shooting, his quality in his dribbling, and his ability to use both feet are qualities I've admired in the past.
"He's destined to grow further and will be an added value for Bayern's future."